Does "holy brethren, partakers of the heavenly calling" and "whose house are we" (Hebrews 3:1, 6) refer to believers or unbelievers?

We cannot accept that these words are addressed to unbelievers for two very obvious reasons.

The nation of Israel never had a heavenly calling. The covenant with Abraham involved blessing for a heavenly and an earthly seed (Genesis 22:17; Galatians 3:29), but the promise through Jacob to Israel was for an earthly seed (Genesis 32:12). Abraham had heavenly hopes (Hebrews 11:10), but his natural seed had earthly hopes.

Israel is never called "the house of God." His (God's) house in Hebrews 3:2 refers to the tabernacle in which Moses was faithful. To make unbelievers a part of "His (Christ's) own house" is not possible. Therefore the two expressions in the question cannot refer to unbelievers. We believe they were believers saved out of Judaism.

We know the name of this epistle is not divinely inspired, but internal evidence is most convincing that it was written to a people who were very familiar with the law and the Levitical system. The majority of them were true to Christ; some were not and turned back. In 1 Corinthians 10:22, going back to either the idol's temple or the Jewish altar was to provoke the Lord to jealousy. Distinction between the genuine and the false is clear in chapters 3, 6, 10 and 12. The most difficult passage, 5:11 to 6:10, becomes much easier to understand if we see the contrast between "they - them" referring to apostates, and .us - you", referring to genuine believers. "Beloved, we are persuaded better things of you, and things that accompany salvation." (6:9).